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Statistical dynamics with thermal noise. (English) Zbl 0822.60093

Etheridge, Alison (ed.), Stochastic partial differential equations. Proceedings of an ICMS workshop held in Edinburgh, UK in March 1994. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 216, 262-286 (1995).
Summary: We consider how to add noise to a nonlinear system in a way that obeys the laws of thermodynamics. We treat a class of dynamical systems which can be expressed as a (possibly nonlinear) motion through the set of probability measures on a sample space. Thermal noise is added by coupling this random system to a heat-particle distributed according to a Gibbs state. The theory is illustrated by the Brussellator, where it is shown that the noise converts a limit cycle into a global attractor. In the linear case it is shown that every Markov chain with transition matrix close to the identity is obtained by coupling to thermal noise with a bistochastic transition matrix.
For the entire collection see [Zbl 0817.00017].

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B31 Stochastic methods applied to problems in equilibrium statistical mechanics
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